For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

-7x + 8, -12x + 12, -17x + 16, . . .

Possible anwers:
-5x + 4
5x + 4
-5x - 4
5x-4

Answer:

a. i) ∠TUV = 39°

ii) The measure of arc VTS (the minor arc) = 102°

b. The diameter OT of the circle = 12

c. The angle which we can calculate, given ∠MOP, is angle ∠OTM = 51°

i) Arc MVT = 98° and arc MO = 82°

Step-by-step explanation:

The given parameters are;

The radius of the circle = 6

∠SUT = 39°, ∠MOP = 49°

a. i) According to two tangent theory, two tangents that meet at a given point are congruent

Therefore, VU is congruent to SU

Given that PU is congruent to PU by reflexive property and PV = PS = The radius of the circle, we have;

ΔPVU is congruent to ΔPSU by Side Side Side (SSS) rule of congruency

∠SUT ≅ ∠TUV by Congruent Parts of Congruent Triangles are Congruent (CPCTC)

Therefore, ∠SUT = ∠TUV = 39° by transitive property of equality

ii) Arc VTS is the minor arc while arc VOS is the major arc by size

The arc measure that describes arc VTS is the minor arc

iii) From circle theorem, we have that the sum of the angle formed by two tangents and the minor arc equals 180°

Therefore, ∠SUT + ∠TUV + arc VTS = 180°

∴ Arc VTS = 180° - (39° + 39°) = 102°

b. The line segment length that can be calculated based on knowing the radius length includes the length of the diameter OT of the circle

The diameter OT = 2 × The length of the radius

∴ The diameter OT = 2 × 6 = 12

c. The angle ∠MOP, is an interior angle of the right triangle ΔTMO formed by the diameter of the circle, OT, therefore, given that ∠MOP = 39°, we have;

∠OTM = 90° - ∠MOP

∴ ∠OTM = 90° - 39° = 51°

∠OTM = 51°

Therefore, given ∠MOP, we can calculate angle ∠OTM

i) The arc that we can calculate, given ∠MOP are arc MVT and arc MO

Arc MVT = 2 × ∠MOP

∴ Arc MVT = 2 × 49° = 98°

Arc MO = 2 × ∠OTM

∴ Arc MO = 2 × (90° - 49°) = 82°

Answer:

area = 8 × 18 = 144 cm^2

volume 8×18×5 = 720cm^3

Answer:

FH ≈ 15.20

Step-by-step explanation:

Using the Altitude- on- Hypotenuse theorem

(leg of large triangle)² = (part of hypotenuse below it ) × (whole hypotenuse )

FH² = 11 × (11 + 10) = 11 × 21 = 231 ( take the square root of both sides )

FH = [tex]\sqrt{231}[/tex] ≈ 15.20 ( to 2 dec. places )

Answer:

The plane is going 325 kilometers per hour :)

Step-by-step explanation:

To find the average speed per hour, divide 1300 by 4.

1300/4 = 325

Answer:

22= 2(pi)(r)(45/360)

28.01

C=176

Step-by-step explanation:

slope is just "how much up or down" for one step to the right.

its clearly negative here

only -3 seems to be remotely plausible looking at the graph in your screenshot

Answer:

The slope is [tex]-3[/tex]

Step-by-step explanation:

The slope of a line, [tex]m[/tex], that passes through points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

To find the slope of a line, choose two points that it clearly passes through.

In the given graph, the line clearly passes through points (2, 2) and (0, 8).

Let:

[tex](x_1, y_1)\implies (2, 2)\\(x_2, y_2)\implies (0, 8)[/tex]

Substitute into the slope formula:

[tex]m=\frac{8-2}{0-2}=\frac{6}{-2}=\boxed{-3}[/tex]

Therefore, the slope of the line is -3.

Answer:

4√3

Step-by-step explanation:

This is a right triangle. When two sides are given in a right triangle, we need to use the Pythagorean Theorem to solve for the third side.

Pythagorean Theorem: a² + b² = c²

The a here is 11, while the b is x. The c is always the hypotenuse (the longest side), which is 13.

Now we substitute:

11² + x² = 13²

121 + x² = 169

-121           -121

x² = 48

√x² = √48

x = √48 <-- We can simplify that.

√48 = 12 * 4 = 3 * 4 * 4 = 4√3

Hello !

Answer:

[tex]\boxed{\sf x=4\sqrt 3}[/tex]

Step-by-step explanation:

It is a right-angled triangle. To find the value of x, we will have to use the Pythagorean theorem which says that the lengths of the sides of a right-angled triangle satisfy the following equality :

[tex]\boxed{\sf c^2=a^2+b^2}[/tex]

Where :

In this triangle, we can consider a = 11, b = x, and c = 13.

Let's substitute the values of a, b, and c into the formula.

[tex]\sf 13^2=11^2+x^2[/tex]

Now we have to solve the equation to find the value of x.

Let's subtract 11² from both sides and calculate.

[tex]\sf 13^2-11^2=11^2-11^2+x^2\\x^2=13^2-11^2\\x^2=169-121\\x^2=48[/tex]

Reminder : if x² = a (a ≥ 0), then x = ±√a.

Let's apply that to our equation.

[tex]\sf x=\pm \sqrt{48}[/tex]

x represents a distance, it must be positive. The unique solution is:

[tex]\sf x=\sqrt{48}\\\boxed{\sf x=4\sqrt 3}[/tex]

Have a nice day ;)

[tex] \frac{ \sin(20 \degree) }{ \cos(70\degree) } + \frac{ \cos(35\degree) }{ \sin( 65\degree)} [/tex]

[tex] \frac{ \sin(20 \degree) }{ \cos(70\degree) } + \frac{ \cos(35\degree) }{ \sin( 65\degree)} [/tex]

[tex] \sin( \theta) = \cos(90 - \theta) \\ \\ \cos( \theta) = \sin(90 - \theta) [/tex]

So putting down the value

[tex] \frac{ \cos(90 - 20 \degree) }{ \cos(70\degree) } + \frac{ \sin(90 - 35\degree) }{ \sin( 65\degree)} [/tex]

[tex] \frac{ \cos(70\degree) }{ \cos(70\degree) } + \frac{ \sin(65\degree) }{ \sin( 65\degree)} [/tex]

[tex]\frac{\cancel{\cos(70\degree)}}{ \cancel{\cos(70\degree)}} + \frac{\cancel{\sin(65\degree)}}{\cancel{\sin( 65\degree)}} [/tex]

[tex] \frac{1}{1} + \frac{1}{1} \\ 1 + 1 = 2 \: \: ans[/tex]

Answer:

126

Step-by-step explanation:

Answer:

126°

Step-by-step explanation:

x = (87+165)/2

x = 252/2

x = 126

Answered by GAUTHMATH

Answer:

an = 400*(1/2)^(n - 1) which is C is the most common answer.

Step-by-step explanation:

What did you have to do to get 400 as the first term?

There are two answers.

an = 400 * (1/2)^(n - 1)

an = 400 * (1/2)^n

Which one is the answer?

The answer is the one that leaves 400 as the first term.

a1 = 400*(1/2)^(n-1) should be the answer.

400*(1/2)^n  is unfortunately sometimes used. In which case, the first term is a^0

A1 = 400 (1/2)^(n - 1) is the usual for that describes the series.

Answer:

"t" is not a specific thing, this is just the sign of your variable.

t = 4 × 2.5

t = 10

Answer:

Y=7

Step-by-step explanation:

x1 y1  x2 y2

-7 7  3 7

(Y2-Y1) (7)-(7)=   0  ΔY 0

(X2-X1) (3)-(-7)=    10  ΔX 10

slope= 0          

B= 7          

Y =0X +7    

Answer:

y = 7

Step-by-step explanation:

(x₁, y₁) = (-7 , 7)   & (x₂, y₂) = (3 , 7)

y-co-ordinate are same for both points. So, the line parallel to x-axis and it's slope =0

A line that is parallel to x-axis and has a y-intercept 'c' has the equation y = c

y = 7

Answer:

the answer is -10

Step-by-step explanation:

x=x

y=5

then

3x+5y=-5

3x+5*5=-5

3x=-5-25

3x=-30

x=-30/3

•°•x=-10

Answer:

A

Step-by-step explanation:

3x+5*5=-5

x=-10

Answer:

yes

Step-by-step explanation:

in parallelogram ,<A=<C

<C=<D

then <D=115=<C=115

X+115+30=180....TRIANGLE THEROME

X=35

so that,<A=65

<C=65

Answer:

80k

Step-by-step explanation:

let the previous weight be x

88=x + 10%of x

88=x+(10/100)of x

8800=110x

8800/110=x

x=80k

Answer: Original weight = 80 kg

Step-by-step explanation:

Given:

Current weight = 88 Kg

Gain weight rate = 10%

Solve:

Original weight = Current weight / Gain rate

Original weight = (88) / (1 + 10%)

Original weight = 80 Kg

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

Let the number is in the form of aabb.

We can put it as:

The number is a perfect square so it must be divisible by 11.

It is divisible by 11 if (a + b) is divisible by 11..

On the other hand, b = 0, 1, 4, 5, 6, 9 as the last digit of a perfect square.

Also, both a and b must be within (0,9) interval.

Considering the above conditions we have options:

The numbers are:

By testing we confirm only one of them is a perfect square:

Step-by-step explanation:

here's the answer to your question

Answer:

y^(2/3)

Step-by-step explanation:

( y ^ ( 7/3) * y^ ( 1/3)  ) ^ 1/4

Combine the terms in side the parentheses

a^b* a^c = a^(b+c)

( y ^ ( 7/3+ 1/3)  ) ^ 1/4

( y^( 8/3) )^1/4

We know a^b^c = a^(b*c)

y ^(8/3*1/4)

y^(2/3)

If the perimeter is 16' the sum of the length and width must be 8'. Assuming that area is non 0 possible dimensions are:

1x7 2x6 3x5 4x4 5x3 6x2 7x1

Answer:

−7d−8

Step-by-step explanation:

Subtract 8d from d.

Answer:

x = -6 and y = -9

y = 0

Step-by-step explanation:

A vertical line is an x = equation. No matter what y equals, x will always be -6, so it's x = -6. A horizontal line is a y = equation. No matter what x equals, y will always be -9, so it's y = -9. Finally the equation of the x axis is simply y = 0 since any point on that horizontal line has a y coordinate of 0.

Answer:

x = -6 and y = -9

thectgod ig

Answer:

arc GH = 74°

Step-by-step explanation:

The inscribed angle GFH is half the measure of the intercepted arc aGH, then

arc GH = 2 × 37° = 74°

Step-by-step explanation:

LCM of 7 and 5 is 35

now will make the denominator equal,

10+7/35

So, Ram's work = 10/35

Shyam's work = 7/35

so

Ram > Shyam

hope it helps

Answer:

a- 15 b- 1292^cm this is the answer

Answer:

a. 29

b. 3 is added each time

Step-by-step explanation:

In the given rule, n represents the term number. So, when k=2, n would be 1 because it is the first term. Therefore, to find the 10th term, plug 10 in for n, then solve. The equation would look like [tex]k=3(10)-1[/tex] which equals 29.

The pattern for this type of sequence is known as the common difference because it is the amount that is added each term. You know this because when reading the sequence you can see that it is increasing by 3. Additionally, in the rule, 3 is being multiplied by n, this shows that 3 is the common difference/pattern.

Answer:

29

Step-by-step explanation:

Answer:

b, c, d

Step-by-step explanation:

y=kx+b

or

y=kx

so y=5,25x-right

y=0,5x-right

y=2,5x+7-right